Collaborative Research: Strain-limiting Cosserat Rods with Applications to Modeling Biological Fibers

合作研究：应变限制 Cosserat 棒在生物纤维建模中的应用

• 批准号: 2307563
• 负责人: Kumbakonam Rajagopal
• 金额: $ 9.69万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307563&HistoricalAwards=false
• 关键词: Collaborative; Research; Strain; limiting; Cosserat

A vast array of objects encountered throughout science, engineering, and everyday life have two physical dimensions that are much smaller than a third. Examples include collagen fibers, DNA, RNA, beams, pipelines, pencils, and cellphone charger cords. This research project concerns the theory of Cosserat rods: bodies that are parameterized by a curve with two perpendicular directions, the two smaller physical dimensions, specified at each point. This theory models the bodies response to applied forces using partial differential equations, expressing balance of linear momentum, angular momentum, energy, and entropy. The research will investigate and validate a new class of Cosserat rod models, describing the stretch-limiting behavior of biological fibers, including DNA and RNA. Apart from determining the models’ fundamental properties from the mathematical physics point of view, the results of the research will contribute to the understanding and prediction of how fibers bend, twist, and stretch during biological processes. The project will provide research training opportunities for graduate students. The research project will focus on new nonlinear, thermodynamically consistent, strain-limiting constitutive relations between the bending, twisting, and stretching strains and the contact couples and forces in a Cosserat rod. In the static Green elastic setting, the research will include establishing energetic stability and bifurcation results for helical equilibrium states, and the quantitative comparison of predictions to the associated, available, experimental data. In the dynamic viscoelastic setting, the balance equations are a system of parabolic partial differential equations with different field equations, resulting from specifying different dissipation rates. The investigators will focus on obtaining global well-posedness, Lyapunov stability and long-time asymptotic results for solutions to such nonlinear field equations with experimentally natural boundary conditions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

科学、工程和日常生活中遇到的大量物体都具有比三分之一小得多的物理尺寸，例如胶原纤维、DNA、RNA、梁、管道、铅笔和手机充电器线。 Cosserat 杆理论：由具有两个垂直方向的曲线参数化的物体，在每个点指定两个较小的物理尺寸。该理论使用偏微分方程模拟物体对所施加的力的响应，表达线性动量的平衡。该研究将研究并验证一类新型 Cosserat 杆模型，描述生物纤维（包括 DNA 和 RNA）的拉伸限制行为，并从数学物理角度确定模型的基本属性。看来，该研究结果将有助于理解和预测纤维在生物过程中如何弯曲、扭曲和拉伸，该项目将为研究生提供研究培训机会，该研究项目将重点关注新的非线性、热力学一致性。 , 应变限制在静态格林弹性设置下，Cosserat 杆中的弯曲、扭转和拉伸应变与接触力偶和力之间的本构关系，研究将包括建立螺旋平衡状态的能量稳定性和分叉结果，以及预测的定量比较。在动态粘弹性设置中，平衡方程是具有不同场方程的抛物线偏微分方程组，由指定不同的耗散率而产生。全局适定性、李亚普诺夫稳定性和长期渐近结果，用于解决具有实验自然边界条件的此类非线性场方程。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查进行评估，被认为值得支持标准。